Field of the Invention
The present invention relates to a device and a method for coding digital data, a device and a method for receiving digital data and communication devices using them.
This invention is of use in all areas of coding, storage and transmission of digital data, and in particular those using an alphabet in which the number of symbols is different from 4, 16 or 256.
In particular, the present invention applies to transmission of radio data modulated by an amplitude modulation in accordance with two carriers in quadrature (hereinafter called "QAM") with 64 states (hereinafter called "64-QAM").
There are many coding methods allowing error correction of digital data. Among the best known codes used at present, the Reed-Solomon codes may be mentioned. These constitute a powerful means of correcting data transmission errors. They may be constructed on any alphabet containing a number of symbols which is equal to a power, p.sup.m, of a prime number, p.
Very often a value of m equal to 8 and a value of p equal to 2 is chosen. The consequence of this large predominance of codes on alphabets with 2.sup.8 (=256) symbols is that the majority of Reed-Solomon coders and decoders which are found on the market work on this alphabet. Their low relative cost and their high efficiency means that they are used in many areas notably in the transmission or storage of digital data on tape or disc. This is because a Reed-Solomon coder or decoder constructed to work on 2.sup.8 symbols can also work on an alphabet containing 2.sup.4 (=16), 2.sup.2 (=4) or 2.sup.1 (=2) symbols. The corresponding codes are commonly known under the name "BCH codes" on respectively GF(2.sup.4), GF(2.sup.2) or GF(2) (where GF means "Galois Field"). Nevertheless, an alphabet with 64 symbols cannot be treated in this way because the Galois field GF(2.sup.6) is not a sub-field of GF(2.sup.8).
Therefore, when the natural alphabet of an application contains 64 symbols, as in a system using a QAM-64 modulation, these symbols cannot be considered as words of a code on GF(2.sup.8).
Consequently, in the case of transmission of data modulated with a QAM-64 modulation, a person skilled in the art of transmission wishing to use inexpensive Reed-Solomon coding components uses them in a non-optimal way: he considers a sequence of binary data as a flow of octets which he codes with a Reed-Solomon coder. The code words produced are considered with no particular care as a sequence of 6-uples; each 6-uple is finally modulated in the form of a QAM-64 symbol.
On receipt, each symbol received is interpreted as a binary 6-uple. The resulting sequence of binary data is considered as a sequence of octets specifying one GF(2.sup.8) element. This sequence of GF(2.sup.8) elements, entering a Reed-Solomon decoder corresponding to the coder used at transmission, will be decoded in an ordinary manner. This manner of formatting QAM-64 symbols in octets has a significant drawback. As in any transmission system, transmission errors occur on QAM-64 symbols. However, the 6 bits of the same QAM-64symbol may have been coded over two consecutive octets. As the Reed-Solomon decoder works on octets, it is possible that an error on a single QAM-64 symbol could produce an error on two consecutive octets, which amounts to doubling the error affecting the data transmitted in this manner. This reduces the correction capability of a Reed-Solomon coder expressed as a number of correctable QAM-64 symbols.
In order to resolve the problem disclosed above, a code specified on GF(2.sup.6) could be chosen. Two other problems then arise: on the one hand, in this case, a component of this type is not readily found today on general sale. On the other hand, if it is wished to use words of lengths greater than or equal to 64 binary 6-uples, no Reed-Solomon code of this length is known on GF(2.sup.6). Consequently, the redundancy of the codes is used less efficiently; for a given power of correction, a greater redundancy is required (in other words, the efficiency of the code is lower).